Example 4. Use
Picard iteration to find and plot approximations for
the solution of the I.V.P.
.
Solution 4.
Picard iteration for generating the first six approximations is started with the Mathematica command:
![[Graphics:../Images/PicardIterationMod_gr_66.gif]](../Images/PicardIterationMod_gr_66.gif)
We can graph the analytic solution and the Picard iterations.
![[Graphics:../Images/PicardIterationMod_gr_68.gif]](../Images/PicardIterationMod_gr_68.gif)
![[Graphics:../Images/PicardIterationMod_gr_69.gif]](../Images/PicardIterationMod_gr_69.gif)
![[Graphics:../Images/PicardIterationMod_gr_71.gif]](../Images/PicardIterationMod_gr_71.gif)
![[Graphics:../Images/PicardIterationMod_gr_72.gif]](../Images/PicardIterationMod_gr_72.gif)
![[Graphics:../Images/PicardIterationMod_gr_74.gif]](../Images/PicardIterationMod_gr_74.gif)
![[Graphics:../Images/PicardIterationMod_gr_75.gif]](../Images/PicardIterationMod_gr_75.gif)
(c) John H. Mathews 2005